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Globally solvable systems of complex vector fields. (English) Zbl 1242.35092
Summary: We consider a class of involutive systems of \(n\) smooth vector fields on the \(n+1\) dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

MSC:
35F05 Linear first-order PDEs
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
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